Abstract: Cao's splitting theorem says that for any complete Kähler-Ricci flow with , simply connected and nonnegative bounded holomorphic bisectional curvature, is holomorphically isometric to , where is a Kähler-Ricci flow with positive Ricci curvature for . In this article, we show that , where is the Ricci rank of the initial metric. As a corollary, we also confirm a splitting conjecture of Wu and Zheng when curvature is assumed to be bounded.